Cook bacon in a large straight-sided skillet over medium heat until crisp and browned, about 8 minutes. Transfer to paper towels. Remove fat from skillet.Advertisement
Cook pasta in a large pot of generously salted boiling water until al dente, about 2 minutes less than package instructions. Reserve 1 cup pasta water; drain. Meanwhile, heat 2 tablespoons oil in skillet over medium-high. When it shimmers, add onion, zucchini, and basil sprigs; season with salt and pepper. Cook, stirring occasionally, until vegetables are tender and golden brown in places, about 8 minutes.
Reduce heat to medium; stir in remaining 1 tablespoon oil, corn kernels and milk, tomatoes, garlic, and jalapeño. Cook just until garlic is fragrant and tomatoes begin to release their juices, 1 to 2 minutes. Add vinegar; cook 30 seconds more. Add pasta and 1/2 cup reserved pasta water; continue to cook, tossing, until sauce thickens slightly and clings evenly to pasta, 2 to 3 minutes. Remove from heat; remove and discard basil sprigs. Stir in cheese. If needed, add more pasta water, a little at a time, until sauce evenly coats pasta again. Serve, topped with bacon, a drizzle of oil, more cheese, and basil leaves.
If using a large zucchini instead of two small ones, quarter it length-wise before slicing crosswise. Use the side of a spoon to scrape the corn milk from the cobs.